# Tagged Questions

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### Calculate the expected return, variance and standard deviation [on hold]

Calculate the expected return, variance and standard deviation for the following portfolio of four stocks Stock1 16.4% return Stock2 -9.2% return Stock3 7.9%return Stock4 ...
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### Measuring variation of one data set with respect to another data set

Each of the points in the plot below is a mean of 1000 samples. The standard deviation of a point on the RED line is "small" in that it is smaller than the difference between the mean of the RED line ...
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### What does it mean for variances to be equal?

What does it mean for variances to be equal? Is this the same as the variance to follow a normal distribution?
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### Variance of a sample - proof

On page 72 of Introductory Statistics, A Conceptual Approach Using R (Routledge, 2012), the authors first compute the variance of a sample of size $n$ using: ...
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### Setting intercept to zero: Will this change both standard deviations and the error term?

After running a single regression with a forced zero intercept, I understand that $\beta$ (slope(s)) will change as $\alpha$ (intercept) will be set to zero. Easy. $\rho = \beta(\sigma_x / \sigma_y)$ ...
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### Demand with different Measurement

Weekly's demand of a product has a probability function ...
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### Quantifying heterogeneity

I have been trying to quantify the heterogeneity of a given variable. I'd like to say that the distribution in calcite concentrations, for example, is more heterogeneous in one rock formation than ...
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### Estimating the population variance [duplicate]

I'm trying to understand the emphasized phrase in the following passage: The usual method of determining the probability that the mean of the population lies within a given distance of the mean of ...
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### Standard deviation of binned observations

I have a dataset of sample observations, stored as counts within range bins. e.g.: min/max count 40/44 1 45/49 2 50/54 3 55/59 4 70/74 1 Now, ...
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### Variance of superset from variance of subsets [duplicate]

Let's say I want to estimate $var(A)$ of a list of numbers $a_i \in A, i\in [0,N]$. However, I only have the variance of the non-overlapping, and complete ($B \cup C = A)$ subsets $B$ and $C$. ...
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### How to quantify the effect of an independent variable on the standard deviation of the dependent variable?

My independent variable changes the variation in the dependent variable. The mean doesn't matter, just the variance. Bartlett and Levene's tests indicate a small p-value and thus significant ...
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### Population Variance and Sample Variance

How is it that lowering the number of frequence,$n$ by $1$ in the for formula for Population and Sample Variance account for the discrepency of using sample rather than population. I mean how is ...
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### Prove one assumption in confidence interval for difference in means

How to prove that $\sqrt{( s_1^2 / n_1 + s_2^2 / n_2)}$ converge in probability to $\sqrt{( \sigma_1^2 / n_1 + \sigma_2^2 / n_2)}$? $s^2$ converge in probability to $\sigma^2$, when n goes to ...
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### Combining and ranking standard deviations

I am trying to take three independent indicators and combine them into a single composite measure. For discussion, let's say that this is a composite measure for 'economic performance', and that the ...
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### Why does GARCH use squared residuals?

Take GARCH(1,1). Suppose the mean equation is: $$y_t = \mu + \epsilon_t = \mu + z_t\sigma_t$$ with $z_t \sim N(0,1)$, $\epsilon_t \sim N(0,\sigma_t)$. Then the univariate GARCH(1,1) variance ...
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### Variance of a bounded random variable

Suppose that a random variable has a lower and an upper bound [0,1]. How to compute the variance of such a variable?
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### Variance or standard deviation from a value other than the mean

Is there a term(s) for calculating the variance or standard deviation from a value other than the mean? Example: If I have a set of estimates for jelly beans in a jar, calculating standard deviation ...
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### Are $\sigma_{70\%} = cte * \sigma /\sqrt{N}$, & $\sigma_{\bar x_{70\%}} = cte * \sigma /\sqrt{N}$ valid with non-normal distributions?

My working population is non normally distributed and from time to time I need to take a sample of it. Sometimes my sample exists of 100 units, at other times of 150 units. Of my sample I calculate ...
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### What's the difference between variance and standard deviation?

I was wondering what's the difference between variance and standard deviation? If you calculate it its is clear that you get the standard deviation out of the variance... But what does that mean in ...
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### Size of the data set for measuring variation

This might be a simple question but I am unable to find a solution on the web. I would like to measure variation of some numerical data. What is the minimum number of values I should use for measuring ...
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### What does a squared coefficient of variation signify?

The coefficient of variation is defined as the ratio of S.D to mean, a dimensionless number which on multiplication by 100 gives the percentage of dispersion with mean. But when we square this ...
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### How do I test whether differences in populations are significant?

I'm working on a large database. I want to explore whether certain batch jobs run in more or less time after a change was than they did before the change. There are about 90 distinct batch jobs. They ...
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### Is 2-sigma limit applicable as a measure of variance to a distribution?

There is a paper that uses something like the 2-sigma limit to check if a quantity is more-or-less constant. More specifically in this paper on Text Detection (Sec. 3.2 3rd para last line) this limit ...
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### Estimate variance of sub-sets from overall variance

I am looking for a way to estimate the variance of a summed sub-set based on the variance of those sums. Si = sum( Ai ) S = { S0...Sn } V = variance( S ) That ...
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### Maximum value of coefficient of variation for bounded data set

In the discussion following a recent question about whether the standard deviation can exceed the mean, one question was raised briefly but never fully answered. So I am asking it here. Consider a ...
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### Understanding “variance” intuitively

What is the cleanest, easiest way to explain someone the concept of variance? What does it intuitively mean? If one is to explain this to their mom or child how would one go about it? It's a concept ...
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### Comparing standard deviations between variables with very different ranges

I have a number of variables for which I want to compare the standard deviations. Each of these variables is actually the data for a particular wavelength of light, and I want to produce a plot ...
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### Bound on variance of sum of variables

Suppose I have two finite sets of data A and B, with equal length n. What's the best upper ...
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### How should I characterize the “typical” variance of a large collection of variables?

For an experiment I'm analyzing, I took many measurements of many different values. (To make it concrete, let's pretend I measured the height of people from many different age groups -- I have the ...
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### Relationship between number of replications and the standard deviation of entry means

I'm working at a plant breeding company. During some spare time I recently did some exploring of our data (yield trials), mostly just out of curiosity and wanting to learn R better. I started by ...
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### Computing descriptives statistics for sites and locations based on literature search with sites having varying numbers of time points

I've collected a data set from the literature. These data are largely binomial: they are clutch sizes of a bird that lays only 1 or 2 eggs in most areas, and in some areas will lay 3. However the only ...
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### When would it be appropriate to report variance instead of standard deviation?

I have conducted an analysis in which I have modeled different variance components. When reporting the results in a table, it is much more concise to report standard deviations instead of variances. ...
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### How to calculate the difference of two standard deviations?

Background I have two estimates of variance and their associated standard errors calculated from sample sizes of $n=500$ and $n=10,000$ the results are $\hat{\sigma^2} (sd_{\hat{\sigma^2}})$: ...
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### Given sample size, group means, and misc. post-hoc range statistics, can you suggest a good way to estimate variance through simulation?

I previously asked this question about the validity of my solutions for for $SE$ given $n$, $\bar{X_i}$ and summary statistics from post-hoc multiple comparisons such as Fisher's $LSD$ and Tukey's ...
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### Pitman's test of equality of variance and testing for regression to the mean: am I doing the right thing?

I have 2560 paired observations from an experiment in which participants provided two ratings for a set of objects, at two different points in time. Half of the objects in the set had the value of an ...
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### Basic question regarding variance and stdev of a sample

Suppose there is a very big (infinite?) population of normally distributed values with unknown mean and variance. Suppose also that we have a sample, S, of n values from the entire population. We can ...
I have a set of $N$ bodies, which is a random sample from a population whose mean and variance I want to estimate. A property of each body is being measured $m_i$ times ($m_i>1$) and different for ...